1. Technical Field
The invention relates to differential measurement of mass. More particularly, the invention relates to the use of precision weighing to monitor the thickness and uniformity of deposited or etched thin films.
2. Description of the Prior Art
Measurement tools are used in many manufacturing processes to monitor the thickness and uniformity of deposited or etched thin films. For example, optical interference techniques are commonly used to monitor insulating films, while resistive techniques are generally employed to monitor conductive films.
Resistive techniques are destructive in nature, for example the 4-point probe process uses probes having sharp points to measure the resistance of a deposited or etched film, and therefore cannot be used to measure production samples. Such resistive techniques are used to calculate film thickness based upon the assumed resistivity of the film. However, the thin film resistivity is not necessarily related to the bulk film value, nor is such correlation easily predictable.
Eddy current tools may also be used to monitor conductive films. See, for example W. Rodgers, Thin Film Thickness Measuring Apparatus Using An Unbalanced Inductive Bridge, U.S. Pat. No. 3,878,457 (15 Apr. 1973); and W., Smoot, Resonant Frequency Measuring Device For Gauging Coating Thickness, U.S Pat. No. 4,005,359 (25 Jan. 1977). While eddy current techniques are not destructive, such techniques have other disadvantages with patterned production samples. For example, eddy current techniques are sensitive to pattern shapes and thus produce differing results for films having similar resistivities but different topographies.
It is common in the semiconductor industry to use a balance to monitor the average thickness of metal films, for example tungsten films that are deposited using low pressure chemical vapor deposition ("LPCVD"). A balance is also employed to monitor the thickness of epitaxial silicon deposition processes. Knowledge of the sample area and the film density are necessary to convert mass measurements made using a balance to an average thickness measurement. These variables are relatively straightforward to predict.
A time delayed differential weighing procedure may be used to calculate the change in mass of a sample after it has been processed. Such processing may involve adding material to or removing material from a sample, and may require a significant amount of time, e.g. more than 15 minutes, to complete. Examples of relevant processes include deposition, etching, plating and corroding.
An important aspect of the invention is to provide a weighing procedure in which maximum precision and accuracy is achieved. A time delayed differential weighing is a more complex weighing procedure than a simple differential measurement. This additional complexity is a result of compensating for changes in environmental conditions between the two times the measurements are executed, i.e. before and after sample processing. For example, changes in temperature and air density, i.e. buoyancy, give rise to errors that would not occur if the second measurement was made immediately following the first measurement, as is the case with a simple differential measurement.
There are various extrinsic sources of error when weighing a sample. These errors increase in number and relevance as the reproducibility requirements of the process become more restrictive. For example, as described above, a time delayed differential measurement is subject to error because the environmental conditions are not the same at the time the two measurements are made, i.e. temperature and air density vary over time. Additionally, a differential measurement is subject to an intrinsic error relating to the difference calculation. The magnitude of this error may be on the order of 1.41 times greater than the error of either component, which is the typical error associated with adding or subtracting two values, where each value has an error component. Calculating the change in mass also introduces an error related to converting the first reading to what it would be at the temperature and air density at the time of the second reading. Human errors, referred to as appraiser variation (i.e. a quantitative measure of the reproducibility), are also introduced when the various measurements are made. Another common source of error that results in poor balance reproducibility is introduced when a balance is used after being dormant for a number of hours. i.e. the balance may produce slightly different readings as it "warms up."
Temperature and air density errors should not be ignored when using a four or five place balance (i.e. a balance that measures in grams to four or five digits to the right of the decimal point respectively) because the mass of the substrate greatly exceeds the mass of the etched or deposited film. Once the substrate errors are minimized, temperature and air density thin film errors may be ignored when using a four place balance, if desired, because the intrinsic reproducibility of the balance is not significantly eroded by these errors, although the balance must be periodically calibrated. On the other hand, the superior precision of a five place balance is degraded by ignoring these thin film error sources. Additionally, the dormancy error also significantly degrades all types of electronic analytical balance measurements.
Air density, temperature, balance reading, and dormancy errors are now examined.
The weight of a sample measured in air differs from the weight of the sample when measured in a vacuum by an amount proportional to the quantity of displaced air. This buoyancy phenomenon was first explained by Archimedes. In the various applications for which a differential weighing procedure is used, a long time may elapse between the first weighing of the sample before the sample is processed, and a second weighing of the sample after sample processing, e.g. 15 minutes to more than one day. During this processing interval, there are typically changes in the air density and temperature.
Modern electronic analytical balances only partially compensate for the air density related error because the density of the sample, and to a much lesser extent the etched or deposited film, almost always differ from the density of the internal calibration weights in the balance. Thus, the standard calibration procedure cannot completely compensate for changes in air density because the sample density is not identical to that of the internal calibration weights, which are typically made of an iron alloy having a density of about 8.0 g/cm.sup.3.
The actual mass of the sample also differs from the balance reading because of temperature related errors. There is generally a 1-2 PPM/.degree.C. error relating to the balance electronics. For example, the largest component of the error for electromagnetic force compensation balances is the change in the magnetic field of the electromagnet due to temperature variation. It is necessary to quantify the magnitude of the temperature related error by examining the temperature calibration procedure capabilities of electronic analytical balances.
Manual balance operation relies on a balance operator to record a displayed stable balance result. Depending on the balance parameters that are chosen, this value can vary significantly from one operator to another. For example, one operator might record the result immediately after stability is indicated, while another operator might wait for five additional seconds before recording the result. A lack of operator concentration can also produce a variation in this waiting period.
When a balance is used after being dormant for a number of hours, the operator usually "warms up" the balance by loading and unloading a sample numerous times before the actual measurements are recorded. The dormancy phenomenon is thought to be the result of static frictional forces acting on the balance weighing mechanism. However, the exact mechanism that gives rise to the dormancy phenomenon is not entirely understood, and there is thus no consensus at this time on the cause of this problem. One problem with this sequence of steps is the potential for significant appraiser variation, i.e. different operators may not perform the balance warm up procedure adequately or the same way.
The known time delayed differential weighing technique involves calibrating the balance immediately preceding both sets of measurements to compensate for temperature variations. The weighing procedure also requires the measurement of the temperature, pressure, and relative humidity to calculate the air density at the time of each set of measurements to compensate for changes in air density. The known procedure is also subject to various appraiser errors that can produce inconsistent results.
It would therefore be a significant contribution to the art to develop an improved weighing procedure, including associated hardware, that minimizes many of the problems associated with loading a sample onto a standard electronic analytical balance, and with using such balance to make a time delayed differential measurement.